Highest Common Factor of 6327, 3774, 77786 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 6327, 3774, 77786 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6327, 3774, 77786 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 6327, 3774, 77786 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 6327, 3774, 77786 is 1.

HCF(6327, 3774, 77786) = 1

HCF of 6327, 3774, 77786 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 6327, 3774, 77786 is 1.

Highest Common Factor of 6327,3774,77786 using Euclid's algorithm

Highest Common Factor of 6327,3774,77786 is 1

Step 1: Since 6327 > 3774, we apply the division lemma to 6327 and 3774, to get

6327 = 3774 x 1 + 2553

Step 2: Since the reminder 3774 ≠ 0, we apply division lemma to 2553 and 3774, to get

3774 = 2553 x 1 + 1221

Step 3: We consider the new divisor 2553 and the new remainder 1221, and apply the division lemma to get

2553 = 1221 x 2 + 111

We consider the new divisor 1221 and the new remainder 111, and apply the division lemma to get

1221 = 111 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 111, the HCF of 6327 and 3774 is 111

Notice that 111 = HCF(1221,111) = HCF(2553,1221) = HCF(3774,2553) = HCF(6327,3774) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 77786 > 111, we apply the division lemma to 77786 and 111, to get

77786 = 111 x 700 + 86

Step 2: Since the reminder 111 ≠ 0, we apply division lemma to 86 and 111, to get

111 = 86 x 1 + 25

Step 3: We consider the new divisor 86 and the new remainder 25, and apply the division lemma to get

86 = 25 x 3 + 11

We consider the new divisor 25 and the new remainder 11,and apply the division lemma to get

25 = 11 x 2 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 111 and 77786 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(25,11) = HCF(86,25) = HCF(111,86) = HCF(77786,111) .

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Frequently Asked Questions on HCF of 6327, 3774, 77786 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 6327, 3774, 77786?

Answer: HCF of 6327, 3774, 77786 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6327, 3774, 77786 using Euclid's Algorithm?

Answer: For arbitrary numbers 6327, 3774, 77786 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.